1. Field of the Invention
The present invention relates generally to reservoir flow simulation, and more particularly to methods for upscaling from fine-scale earth models to produce coarse-scale reservoir simulation models.
2. Description of the Related Art
Upscaling is often needed in reservoir simulation to coarsen highly detailed geological descriptions, for example to enable fast flow simulation in complex systems. For this purpose, a number of upscaling procedures have been developed and applied. These techniques generally take as their starting point a fine-scale geological model of the subsurface. The intent is then to generate a coarser model that retains a sufficient level of geological realism of the underlying fine-scale description, for use in flow simulation. Though model sizes can vary substantially depending on the application, typical fine-scale geocellular models may contain on the order of 107-108 cells, while typical simulation models may contain on the order of 104-106 blocks.
A variety of upscaling techniques exist and these can be categorized in different ways. One important distinction is in terms of the coarse-scale parameters that are computed by a particular method. Specifically, a technique that generates only upscaled single-phase parameters (i.e., permeability or transmissibility) can be classified as a single-phase upscaling procedure, even though it may be applied to two or three-phase flow problems. A method that additionally generates upscaled relative permeability functions is termed a two-phase upscaling procedure. Another way to distinguish upscaling procedures is according to the problem solved to determine the coarse-scale parameters. In particular, methods may be classified as local, extended local, quasi-global or global (in order of increasing computational effort) depending on the problem solved in the upscaling computations. In general, two-phase upscaling methods are more computationally expensive than single-phase upscaling procedures, as a time-dependent two-phase flow problem must be solved in this case.
In cases where two-phase upscaling is performed, the bulk of the overall computation time (i.e., upscaling plus flow simulation) may be spent in the determination of the coarse-scale two-phase flow functions. Thus it would be very useful to accelerate these upscaling computations. This is particularly desirable in cases with substantial uncertainty in the underlying geological model, in which case many realizations (or scenarios) are to be simulated. In such cases, realization by realization agreement between fine and coarse models is less essential. Rather, what is required in this case is agreement of a statistical nature, for example, agreement in the cumulative distribution functions (or the P10, P50, P90 predictions) for relevant production quantities such as cumulative oil recovered or net present value. The required level of accuracy of the upscaling could be slightly less for such cases, though the method should be unbiased and should provide accurate estimates of the required quantities.